A375987 Expansion of e.g.f. (1 + 2 * log(1 - x))^(3/2).

1, -3, 0, 6, 42, 318, 2892, 31944, 424596, 6682740, 122318928, 2559121128, 60275236392, 1577894836248, 45427570253712, 1425885338250432, 48443767097018256, 1770703320887526096, 69273368628184075392, 2887794188011931364576, 127778992241790634125984

Offset: 0

Author

Seiichi Manyama, Sep 05 2024

Keywords

• sign
• easy

Crossrefs

Cf. A088500, A367474, A375945, A375953, A375990.

Programs

Maple

A375987 := proc(n)
    add(mul(2*j-3,j=0..k-1)*abs(stirling1(n,k)),k=0..n) ;
end proc:
seq(A375987(n),n=0..30) ; # R. J. Mathar, Sep 06 2024

PARI

a(n) = sum(k=0, n, prod(j=0, k-1, 2*j-3)*abs(stirling(n, k, 1)));

Formula

a(n) = Sum_{k=0..n} (Product_{j=0..k-1} (2*j-3)) * |Stirling1(n,k)|.